Question

The point Q (-5,-9) is rotated -270 about the origin. Select the location of Q’.

Answer 1

To rotate a point \((x, y)\) about the origin by an angle \(-270^\circ\), we can first convert the angle to a positive equivalent angle. Since \(-270^\circ\) is the same as \(90^\circ\) (because \(-270^\circ + 360^\circ = 90^\circ\)), we will rotate the point \(Q(-5, -9)\) by \(90^\circ\) counterclockwise.

The formula for rotating a point \((x, y)\) by \(90^\circ\) counterclockwise about the origin is:

\[
(x, y) \rightarrow (-y, x)
\]

Applying this formula to the point \(Q(-5, -9)\):

\[
Q'(-5, -9) \rightarrow (-(-9), -5) = (9, -5)
\]

Thus, the coordinates of the rotated point \(Q'\) are \((9, -5)\).